The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
How to simplify the expression?
The expression is given as:
[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Apply the power rule of indices
[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Expand the exponents of the expression
[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]
Apply the product rule of indices
[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]
Collect like terms
[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]
Evaluate the differences
[tex]x^{0-0 - 0[/tex]
This gives
[tex]x^{0[/tex]
Evaluate the exponent
1
Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
Read more about simplifying expressions at:
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